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Quantifying the Likelihood of False Positives: Using Sensitivity Analysis to Bound Statistical Inference

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Objective Criminologists have long questioned how fragile our statistical inferences are to unobserved bias when testing criminological theories. This study demonstrates that sensitivity analyses offer a statistical approach to help assess such concerns with two empirical examples—delinquent peer influence and school commitment. Methods Data from the Gang Resistance Education and Training are used with models that: (1) account for theoretically-relevant controls; (2) incorporate lagged dependent variables and; (3) account for fixed-effects. We use generalized sensitivity analysis (Harada in ISA: Stata module to perform Imbens’ (2003) sensitivity analysis, 2012; Imbens in Am Econ Rev 93(2):126–132, 2003) to estimate the size of unobserved heterogeneity necessary to render delinquent peer influence and school commitment statistically non-significant and substantively weak and compare these estimates to covariates in order to gauge the likely existence of such bias. ResultsUnobserved bias would need to be unreasonably large to render the peer effect statistically non-significant for violence and substance use, though less so to reduce it to a weak effect. The observed effect of school commitment on delinquency is much more fragile to unobserved heterogeneity. Conclusion Questions over the sensitivity of inferences plague criminology. This paper demonstrates the utility of sensitivity analysis for criminological theory testing in determining the robustness of estimated effects.
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Vol.:(0123456789)
Journal of Quantitative Criminology (2019) 35:631–662
https://doi.org/10.1007/s10940-018-9385-x
1 3
ORIGINAL PAPER
Quantifying theLikelihood ofFalse Positives: Using
Sensitivity Analysis toBound Statistical Inference
KyleJ.Thomas1· JeanMarieMcGloin2· ChristopherJ.Sullivan3
Published online: 22 June 2018
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract
Objective Criminologists have long questioned how fragile our statistical inferences are to
unobserved bias when testing criminological theories. This study demonstrates that sensi-
tivity analyses offer a statistical approach to help assess such concerns with two empirical
examples—delinquent peer influence and school commitment.
Methods Data from the Gang Resistance Education and Training are used with models
that: (1) account for theoretically-relevant controls; (2) incorporate lagged dependent vari-
ables and; (3) account for fixed-effects. We use generalized sensitivity analysis (Harada in
ISA: Stata module to perform Imbens’ (2003) sensitivity analysis, 2012; Imbens in Am
Econ Rev 93(2):126–132, 2003) to estimate the size of unobserved heterogeneity neces-
sary to render delinquent peer influence and school commitment statistically non-signifi-
cant and substantively weak and compare these estimates to covariates in order to gauge
the likely existence of such bias.
Results Unobserved bias would need to be unreasonably large to render the peer effect
statistically non-significant for violence and substance use, though less so to reduce it to a
weak effect. The observed effect of school commitment on delinquency is much more frag-
ile to unobserved heterogeneity.
Conclusion Questions over the sensitivity of inferences plague criminology. This paper
demonstrates the utility of sensitivity analysis for criminological theory testing in deter-
mining the robustness of estimated effects.
Keywords Sensitivity analysis· False positives· Unobserved bias· Theory testing
“A fragile inference is not worth taking seriously. Leamer (1985)
* Kyle J. Thomas
thomaskj@umsl.edu
1 University ofMissouri-St. Louis, 1 University Blvd, 331 Lucas Hall, St.Louis, MO63121, USA
2 University ofMaryland, CollegePark, MD, USA
3 University ofCincinnati, Cincinnati, OH, USA
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Low self-control Gottfredson and Hirschi (1990) view propensity for delinquent conduct as a direct function of one's self-control. The G.R.E.A.T. data contains eight items that are a subset of the Grasmick, Tittle, Bursik, and Arneklev (1993) self-control scale (see also Thomas, McGloin, & Sullivan, 2018). On a Likert-scale ranging from 1 ¼ strongly disagree to 5 ¼ strongly agree, respondents are asked how much they agree with the following statements: "I often act on the spur of the moment," "I do what brings me pleasure here and now," "I don't devote a lot of thought and effort preparing for the future," "I am more concerned with what happens to me in the short run than in the long run," "I like to test myself every now and then by doing something a little risky," "Sometimes I will take a risk just for the fun of it," "I sometimes find it exciting to do things for which I might get in trouble," and "excitement and adventure are more important to me than security." ...
... Individuals were told to think about their mother or mother-figure and asked to rate the following statements: "can talk about anything," "always trusts me," "knows all my friends," "always understands me," "always ask her for advice," and "always praises me when I do well." Responses ranged from 1 to 7, and higher values are indicative of higher levels of attachment (see Thomas et al., 2018). The maternal attachment items have high interitem reliability across all waves (Wave 1: a ¼ .826; ...
... We measure school commitment using four Likert-scale items that ask respondents how much they agree with the statements: "I try hard in school," "Education is so important that it's worth it to put up with things about school that I don't like," "In general, I like school," and "I usually finish my homework." Response options ranged from 1 ¼ strongly disagree to 5 ¼ strongly agree, with higher values reflecting higher levels of commitment to school (see Thomas et al., 2018). The items demonstrate high inter-item reliability across all waves (Wave 1: a ¼ .735; ...
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A longstanding debate in criminology concerns whether peers influence delinquency or if they are of no significance because criminal propensity develops independent of associations. Matza (1969 Matza, D. (1969). Becoming deviant. New Brunswick: Transaction. [Google Scholar]) criticized these competing perspectives, suggesting instead that the peer–delinquency relationship is nuanced, such that there is both between- and within-person variability in the influence of friends. Drawing on his choice-based perspective, we hypothesize that peers have a stronger influence on the delinquent tendencies of individuals low in criminal propensity. Further, we predict that the influence of peers varies within-individuals across crime types, such that delinquent friends are less influential for behaviors that individuals anticipate more guilt. Using data from the Gang Resistance Education and Training (G.R.E.A.T.) evaluation, we find support for these hypotheses. Perceived peer delinquency is a stronger predictor of offending for those lower in criminal propensity. Further, individuals are less susceptible to delinquent peers for acts in which they anticipate higher levels of guilt.
... Fixes to such violations are well-known and some more advanced fixes are presented in this issue (e.g. Moody and Marvell 2020;Thomas et al. 2019). Some less well-known model assumptions are equally important. ...
... Table 4 provides a series of suggestive steps that can be applied during the process of defining peer influence and in determining the best analytic approach to use to address these questions (for additional reading on the importance of definitions of peer influence see Kindermann & Skinner, 2019). We also suggest that scholars carefully consider recent work indicating that conventional statistical tools do not overestimate influence effects compared with network approaches (Ragan et al., 2019) and influence effects attained from cross-lagged models are unlikely to be false positives derived from unobserved variable biases (Thomas et al., 2019). ...
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